Missing Book

An ISBN is a code used to identify a book uniquely. It consists of 13 decimal digits. What's interesting is its last digit that is computed using the formula

\[r = 10 - ((d_1+3d_2+d_3+3d_4+\dots + d_{11} + 3d_{12}) \mod 10)\]

Then,

\[d_{13} = \begin{cases} r & \quad \text{if } & \quad r < 10 \\ 0 & \quad \text{if } & \quad r = 10 \end{cases}\]

Alice told Bob that she published a book with an ISBN of \(9781400828678\). Is the ISBN number valid?

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